Four Zeros of a Lower Envelope

★ 8/10functions Quadratic Equations algebra Discriminant

Problem

Let $f_t(x)=(x-t)^2-t$ ( $t\in\mathbb R$ ), and for $a<b$ define

f(x)=\begin{cases}f_a(x),&f_a(x)<f_b(x),\\ f_b(x),&f_a(x)\geqslant f_b(x).\end{cases}

If the function $y=f(x)+x+a-b$ has four zeros, find the range of $b-a$ .

Answer

Solution

Difficulty	8/10
Topics	functions, Quadratic Equations, algebra, Discriminant

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